12 research outputs found
Entanglement in composite bosons realized by deformed oscillators
Composite bosons (or quasibosons), as recently proven, are realizable by
deformed oscillators and due to that can be effectively treated as particles of
nonstandard statistics (deformed bosons). This enables us to study quasiboson
states and their inter-component entanglement aspects using the well developed
formalism of deformed oscillators. We prove that the internal entanglement
characteristics for single two-component quasiboson are determined completely
by the parameter(s) of deformation. The bipartite entanglement characteristics
are generalized and calculated for arbitrary multi-quasiboson (Fock, coherent
etc.) states and expressed through deformation parameter.Comment: 5 pages; v2: abstract and introduction rewritten, references adde
A mathematical framework for critical transitions: normal forms, variance and applications
Critical transitions occur in a wide variety of applications including
mathematical biology, climate change, human physiology and economics. Therefore
it is highly desirable to find early-warning signs. We show that it is possible
to classify critical transitions by using bifurcation theory and normal forms
in the singular limit. Based on this elementary classification, we analyze
stochastic fluctuations and calculate scaling laws of the variance of
stochastic sample paths near critical transitions for fast subsystem
bifurcations up to codimension two. The theory is applied to several models:
the Stommel-Cessi box model for the thermohaline circulation from geoscience,
an epidemic-spreading model on an adaptive network, an activator-inhibitor
switch from systems biology, a predator-prey system from ecology and to the
Euler buckling problem from classical mechanics. For the Stommel-Cessi model we
compare different detrending techniques to calculate early-warning signs. In
the epidemics model we show that link densities could be better variables for
prediction than population densities. The activator-inhibitor switch
demonstrates effects in three time-scale systems and points out that excitable
cells and molecular units have information for subthreshold prediction. In the
predator-prey model explosive population growth near a codimension two
bifurcation is investigated and we show that early-warnings from normal forms
can be misleading in this context. In the biomechanical model we demonstrate
that early-warning signs for buckling depend crucially on the control strategy
near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio